Differential equations : an introduction with mathematica微分方程
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作者： Clay C. Ross 著
出 版 社：
出版时间：字数：版次：页数： 431印刷时间：开本： 16开印次：纸张： 胶版纸I S B N ： 9780387212845包装： 精装内容简介
This introductory differential equations textbook presents a convenient way for professors to integrate symbolic computing into the study of differential equations and linear algebra. Mathematica provides the necessary computational power and is employed from the very beginning of the text. Each new idea is interactively developed using it.
After first learning about the fundamentals of differential equations and linear algebra, the student is immediately given an opportunity to examine each new concept using Mathematica. All ideas are explored utilizing Mathematica, and though the computer eases the computational burden, the student is encouraged to think about what the computations reveal, how they are consistent with the mathematics, what any conclusions mean, and how they may be applied.
This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.
作者简介
Dr.Clay Ross Taught mathematics at the university level from 1967through his retirement in may of 2003,he continues to pursue his interests in mathematics,travel,and nature pho-tography;still plays in the university orchestra;and serves as organist at his church.those activities and much reading keep him productively occupied.
目录
Preface
About Differential Equations
1.0 Introduction
1.1 Numerical Methods
1.2 Uniqueness considerations
1.3 Differential Inclusions （Optional）
2 Linear Atgehca
2.0 [atxoduction
2.1 Familiar Linear Spaces
2.2 Abstract Linear Spaces
2.3 Differential Equations from Solutions
2.4 Characteristic Value Problems
3 First-Order Differential Equations
3.0 Introduction
3.I First-order Linear Differential Equations
3.2 Lineax Equations by mathematica
3.3 Exact Equations
3.4 Variables Separable
3.5 Homogeneous Nonlinear Differential Equations
3.6 Bernoulli and Riccati Differential Equations (Optional)
3.7 Clairaut Differential Equations (Optional)
4 Applications of First-Order Equations
4.0 Introduction
4.1 Orthogonal Trajectories
4.2 Linear Applications
4.3 Nonlinear Applications
5 Higher-Order Linear Differential Equations
5.0 Introduction
5.1 The Fundamental Theorem
5.2 Homogeneous Second-Order Linear Constant Coefficients
5.3 Higher-Order Constant Coefficients (Homogeneous)
5.4 The Method of Undetermined Coefficients
5.5 Variation of Parameters
6 Applications of Second-Order Equations
6.0 Introduction
6.1 Simple Harmonic Motion
6.2 Damped Harmonic Motion
6.3 Forced Oscillation
6.4 Simple Electronic Circuits
6.5 Two Nonlinear Examples (Optional)
7 The Laplace Transform
7.0 Introduction
7.1 The Laplace Transform
7.2 Properties of the Laplace Transform
7.3 The Inverse Laplace Transform
7.4 Discontinous Functions and Their Transforms
8 Higher-Order Differential Equations with Variable Coefficients
8.0 Introduction
8.1 Cauchy-Euler Differential Equations
8.2 Obtaining a Second Solution
8.3 Sums, Products and Recursion Relations
8.4 Series Solutions of Differential Equations
8.5 Series Solutions About Ordinary Points
8.6 Series Solution About Regular Singular Points
8.7 Important Classical Differential Equations and Functions
9 Differential Systems: Theory
9.0 Introduction
9.1 Reduction to First-Order Systems
9.2 Theory of First-Order Systems
9.3 First-Order Constant Coefficients Systems
9.4 Repeated and complex roots
9.5 Nonhomogeneous Equations and Boundary-value problems
9.6 Cauchy-Euler Systems
10 Differential Systems:Applications
References
Index